\section{Case Study: when the forecast is accurate}
As a first case study, we consider the forecast released on 14th January 2021 (Figure \ref{fig:usecase1_forecast}). The sub-seasonal model is able to detect the main trends, if compared to the a-posteriori probabilities deriving from our GMM Model (Figure \ref{fig:usecase1_model}). The initial period is characterized by a very strong AR signal, replaced one week later by a long period of NAO- persistence. The forecast is also able to identify an emerging signal of Scandinavian Blocking, which effectively occurred at the end of the period.

\begin{figure}
    \centering
    \begin{subfigure}{\textwidth}
        \centering
        \includegraphics[width = \linewidth]{imgs/forecast_weights20210114.png}
        \caption{Sub-seasonal Forecast weights of 14th January 2021}
        \label{fig:usecase1_forecast}
    \end{subfigure}
    \begin{subfigure}{\textwidth}
        \centering
        \includegraphics[width = \linewidth]{imgs/model_weights20210114.png}
        \caption{Clustering Probabilities of the GMM Model}
        \label{fig:usecase1_model}
    \end{subfigure}
\end{figure}

The end-product we are able to present is illustrated in Figure \ref{fig:usecase1_anomalies}. The chart is referred to the anomaly in the Wind production of power in Germany along the forecasted period. As the Quantification step highlights, the initial presence of AR is particularly favourable for above-normal Wind generation. However, the scope of this tool is to effectively address the trend beyond the first few days, where short-term forecasts would surely be more accurate, especially when referred to the expected magnitude. The presence of NAO- and the subsequent transition to SB are two main drivers for below normal anomalies, which are clearly evidenced by the chart, and correspondingly benchmarked by actual data: in the window between the end of January and the first half of February the production in Germany revelead to be 4GW below normal; during the Blocking persistence was instead 3GW under the average scenario.

\begin{figure}[!htbp]
    \centering
    \includegraphics[width = \textwidth]{imgs/anomalies_20210114_Wind Load Factor.png}
    \caption{Quantification of the Sub-seasonal forecast on the Wind Load Factor Anomaly in Germany}
    \label{fig:usecase1_anomalies}
\end{figure}
Rather than exactly quantifying the shift from the average case, we intend to identify the trend a particular energy variable has in this window of opportunity. For this reason, even when the forecast proves to be performant, it is rarely close to the true observed value.


\section{Case Study: when the forecast is inaccurate}
The strict dependency on the underlying forecasts exposes the main point of weakness of this final step. A totally incorrect forecast, albeit typically rare, is a driver of an as much innacurate quantification. We thus propose a scenario where we identify this occurrence, corresponding to 2nd December 2020.
Comparing the results between our model's prediction and the product of ECMWF (Figures \ref{fig:usecase2_forecast} and \ref{fig:usecase2_model}), the sub-seasonal model is not aligned with the regimes effectively occurred over that period, whereas they are more closely matched by the clustering results evaluated posteriorly.

\begin{figure}
    \centering
    \begin{subfigure}{\textwidth}
        \centering
        \includegraphics[width = \linewidth]{imgs/forecast_weights20201202.png}
        \caption{Sub-seasonal Forecast weights of 2nd December 2020}
        \label{fig:usecase2_forecast}
    \end{subfigure}
    \begin{subfigure}{\textwidth}
        \centering
        \includegraphics[width = \linewidth]{imgs/model_weights20201202.png}
        \caption{Clustering Probabilities of the GMM Model}
        \label{fig:usecase2_model}
    \end{subfigure}
\end{figure}

The calibration and quantification steps in the 45 days window systematically reflect this error. The snapshot is referred to the wind generation occurring in Spain. The below normal generation interesting the vast majority of the forecast turned out to be in reality much above normal, as expected by the NAO- persistence proving to set adequate conditions for extreme wind events in Spain.

\begin{figure}[!htbp]
    \centering
    \includegraphics[width = \textwidth]{imgs/anomalies_20201202_Wind Load Factor.png}
    \caption{Quantification of the Sub-seasonal forecast on the Wind Load Factor Anomaly in Spain}
    \label{fig:usecase2_anomalies}
\end{figure}
